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Senior Projects Fall 2014 Bard Undergraduate Senior Projects
2014
Feature Extraction and Texture Analysis in the
Classication of Paintings
Jacob Fauber
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Recommended Citation
Fauber, Jacob, "Feature Extraction and Texture Analysis in the Classi7cation of Paintings" (2014). Senior Projects Fall 2014. Paper 35.
h8p://digitalcommons.bard.edu/senproj_f2014/35
Feature Extraction and Texture Analysis
in the Classification of Paintings
A Senior Project submitted to
The Division of Science, Mathematics, and Computing
of
Bard College
by
Jacob Fauber
Annandale-on-Hudson, New York
December, 2014
Abstract
Painting classification is a novel subfield of research in computer vision and image process-
ing that focuses on empirically defining a painting’s authorship, date of creation, or genre.
The applications of the subfield have increased in response to changing art markets and
expanding and emerging research. Basic features like color and line in and of themselves
prove inadequate in this study. Texture analysis provides one of the promising additional
features. In this paper, I specifically investigate two different measures of texture analysis,
Gabor filters and Haralick features, in addition to basic features, and their applications
in a specific painting classification problem. I also consider different methods of collecting
this data, and the impact of each on classification.
Acknowledgments
My deepest thanks and gratitude must be paid to the following people:
• My senior project advisor, Keith O’Hara, for his continual academic support, open-
ness, and helpfulness in bringing my rather silly idea to fruition.
• The other members of the Bard Computer Science department, including Rebecca
Thomas, Sven Anderson, and Bob McGrail, for the pivotal role each played in my
education over these four years.
• My family for their unending emotional (and financial) support
• All my extraordinarily understanding friends. You know who you are.
• Any of these artists whose albums are among my senior project playlist, which has
been on constant rotation these past few months:
Beth Orton’s Central Reservation
The Go-Between’s Oceans Apart
The Weepies’ Say I Am You
Antonio Carlos Jobim’s Stone Flower
Sam Phillips’ Don’t Do Anything
Mountains’ Choral
Mouse On Mars’ Niun Niggung
Horace Andy’s Skylarking
Nick Lowe’s The Convincer
Might they serve you as well as they have me.
• And of course, you. Anyone who takes time from their day to read an undergraduate
thesis really deserves an award of some kind, so I guess a dedication will have to do.
Contents
Abstract 1
Acknowledgments 2
1 Introduction 7
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 The Image: Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 The Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Artists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.2 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.3 Potential Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 A Brief Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.1 Feature Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.2 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Previous Work 16
2.1 Features Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Painting Analysis With Gabor Filters . . . . . . . . . . . . . . . . . . . . . 18
3 Feature Extraction 19
3.1 Color Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 RGB & HSV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.2 Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.3 Binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Contents 4
3.2 Edge Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 The Canny Edge Detector . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.2 Line Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Texture and Brushstroke . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.2 Haralick Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.3 Gabor Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.4 Kernel Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 Classification 40
4.1 Random Forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.1 Decision Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.2 Bootstrapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.3 Arboreal Voting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 A Collection Schema . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.1 Generic Model (The Entire Painting) . . . . . . . . . . . . . . . . . . 43
4.2.2 Feature-Dense Model (Quadrants) . . . . . . . . . . . . . . . . . . . 44
4.2.3 Feature-Specific Model (Patches) . . . . . . . . . . . . . . . . . . . . 44
4.3 Feature Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3.1 Individual Features As Classifiers . . . . . . . . . . . . . . . . . . . . 45
4.3.2 Feature Importance . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3.3 The Strong Classifiers . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5 Conclusions 53
5.1 Texture for Painting Classification . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6 Appendix 56
6.1 Data Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.2 Data Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
List of Figures
1.2.1 Convolution about one pixel in image F . . . . . . . . . . . . . . . . . . . . 10
1.2.2 Representations of F, g, and convolution kernel I . . . . . . . . . . . . . . . 10
1.3.1 A sample work from each artist . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.2 Inaccurate edges are detected without blur. See lines in upper left of sub-
figure (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.3 Five distinct samples of Cezanne’s Mont Sainte-Victoire with Large Pine,
taken from Google Images. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.4 The variety between all five images is easily visible in the color histograms. 14
3.1.2 Average color graphs for each artist normalized to 512x512 patch . . . . . . 24
3.2.1 Visual representation of a Guassian blur . . . . . . . . . . . . . . . . . . . . 26
3.2.3 Edge count and edge length for each artist . . . . . . . . . . . . . . . . . . . 28
3.2.4 This patch from The Parc Monceau has over 1000 edges. It might be con-
sidered the most complex patch from Monet’s work. . . . . . . . . . . . . . 29
3.3.1 Potential pixel comparisons for a co-occurrence matrix . . . . . . . . . . . . 31
3.3.3 co-occurrence matrices for each neighbor relationship in g where N
g
= 5 . . 32
3.3.4 Visualization of a Gabor wavelet and its component parts . . . . . . . . . . 36
3.3.5 A simple Gabor kernel, where θ = 0, σ = 1, and frequency is 3 . . . . . . . 37
3.3.6 Original and edge detected image . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.7 Gabor filters operating over four common orientations . . . . . . . . . . . . 38
3.3.8 Gabor filter kernel bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.0.1 Example of individual features for classification . . . . . . . . . . . . . . . . 40
4.1.1 Sample Decision Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 Generic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 Feature-Dense Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.3 Feature-Specific Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
LIST OF FIGURES 6
4.3.1 Accuracy of all pairings of features used in classification . . . . . . . . . . . 47
4.3.2 Graph of all 76 features’ importance measurements for one random forest . 48
4.3.3 Features with the highest importance measurement . . . . . . . . . . . . . . 48
4.3.4 Measure of Correlation as a function of Edge Length . . . . . . . . . . . . . 49
4.3.5 Sum Entropy as a function of Edge Length . . . . . . . . . . . . . . . . . . 50
4.3.6 Sum Entropy as a function of Measure of Correlation . . . . . . . . . . . . . 50
4.3.7 Relatively abnormal paintings from each of the four artists . . . . . . . . . 52
6.2.1 Sample Image from Cezanne The Card Players . . . . . . . . . . . . . . . . 57
6.2.2 Sample Image Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
1
Introduction
1.1 Motivation
The art market is one of the largest unregulated markets in the world. As the economic and
academic uses of art continue to expand, computer analysis of these images can become
very useful. Increasingly accurate categorization may eventually lead to forgery detection
and completed catalogue raisonn´es for artists with dubious history or provenance. As the
art market moves online, automated categorization and analysis can help market paintings
to interested collectors and expand the market.
Though research into general image analysis is plentiful, little work looks specifically at
paintings, and little is understood on how to best categorize them. A suggested but little
studied part of the painting categorization literature is texture analysis, which is used
to capture brushstroke [13]. A more sophisticated knowledge of effectiveness of texture
analysis is useful in these efforts.
1. INTRODUCTION 8
1.2 The Image: Foundations
It is an unfortunate but utterly necessary element of image representation on computers
that the image be digital. Most images used in classification are representations of a non-
digital object, and their representation is digitized. This is an inherently flawed process
(cf. 1.3.3), but serves well enough in representing most images that image processing may
successfully take place.
The following explains what can be expected of a digitized image, and the notation this
paper uses to represent them.
1.2.1 Representation
What does it mean, fundamentally, for an image to be digital? It means the image is
discrete. As such, the image can be broken down into fundamental component parts, in
this case a pixel, and a collection of these represents the image.
There are many ways of representing a pixel. If the image is grayscale, a pixel is almost
universally represented by a byte, an integer value between 0 and 255, which are absolute
black and white, respectively.
To represent color, pixels are generally structured as a tuple, containing various values
which, taken collectively, represent a color value. The significance of these values changes
with respect to the color space. The precise method of pixel representation used for painting
classification varies, and more information can be found in section 3.1.1. There are various
ways of representing a pixel in an image. However, every pixel must have the same method
of representation.
Pixel location will here be represented with simple Cartesian coordinates.
p = (x, y) ∈ R
2
(1.2.1)
1. INTRODUCTION 9
In regards to location, if p = (0,0), that pixel will be located at the top left corner of
the image.
Taken together, at their proper locations with their proper locations, pixels generate
the illusion of a continuous image. The computer, of course, has no concept of continuity;
it understands the image only with respect to contiguousness.
1.2.2 Convolution
After obtaining a digitized image, certain information can be gathered by iterating over
the image matrix and performing calculations on the data. Information like color palette,
mean color value, and color variance can all be understood by performing calculations and
summations over the image proper.
Rather than examining the image itself, a filtering process known as convolution can
occur instead. After this process, there is a new but still relevant image, from which new
information can be learned about the original, such as edge counts, corner locations, and
information density. The act of convolution, in this context, is also known as neighborhood
filtering, and means to generate a new pixel value with respect to that pixel and its
neighbors. The neighboring pixels used depend on the size of the smaller convolution
matrix, called a kernel.
The act of convolution itself will be represented by ∗. The following is the convolution
formula for a 2D signal.
g(x, y) = F ∗ I(x, y) =
N
X
j=−N
N
X
i=−N
F (i, j)I(x − i, y − j) (1.2.2)
The following example shows the appearance of the matrices during convolution of a
single bold data entry p = (1, 1) in the image matrix F.
1. INTRODUCTION 10
F (1, 1) ∗ I = g(1, 1)
45 60 98 127 132
46 65 98 123 126
47 65 96 255 119
47 255 91 107 113
50 59 80 97 110
∗
0.087 0.121 0.087
0.121 0.168 0.121
0.087 0.121 0.087
= 68
Figure 1.2.1: Convolution about one pixel in image F
The appearance of the convolved image matrix for all points (x, y):
F ∗ I = g
45 60 98 127 132
46 65 98 123 126
47 65 96 255 119
47 255 91 107 113
50 59 80 97 110
∗
0.087 0.121 0.087
0.121 0.168 0.121
0.087 0.121 0.087
=
50 67 95 118 128
51 68 106 132 136
68 91 125 133 134
75 97 121 120 123
69 86 98 98 107
Figure 1.2.2: Representations of F, g, and convolution kernel I
1.2.2.1 The Border Case
The one small caveat to convolution is that when faced with the border, where there are
not enough pixel neighbors to fit the standard I(x, y) kernel, a different case must be
met. The standard way of dealing with convolution of borders in this project has been
the reflect case, where outer values are simply ’reflected’ across the image matrix border
to fill the blank spots in the kernel window. All border handling can become problematic,
1. INTRODUCTION 11
but for large enough images the borders become increasingly negligible, as long as their
case is reasonably handled.
1.3 The Data Set
A significant element of the project of painting categorization is simply selecting which
artists and paintings to categorize, and which digitizations of these paintings to consider.
While it is a theoretical nicety that categorization might be generalizable to all artists,
it is undeniable that certain artists are more or less correlated to certain patterns than
other artists, and different artists may tell of their authorship in radically different ways.
For this reason, certain painter pairings have shown themselves to be easier to distinguish
then others [2]. This is part of the significance of artist selection.
1.3.1 Artists
Four artists were used for the categorization project at hand: Cezanne, Monet, Rem-
brandt, and Van Gogh. Artists were chosen partially for their historical importance, but
also bearing in mind variety. Cezanne and Monet were picked, for example, for their pur-
ported similarity in palette and mark, while Rembrandt and Van Gogh were chosen for
their clear distinction in markmaking and palette. It is expected that the classification will
react differently to the comparison of any two of these four artists. An essential aspect of
selection is also the size of each artist’s available catalogue. In this case, between 15 and
20 paintings were used for each artist. 68 images were used in total.
1.3.2 Sources
It is difficult to gather freely available digitized paintings from reputable sources. Un-
reputable sources pose a threat to image stability, with the possibility of, among others,
cropped images, watermarks, and mislabelled information. All images used were there-
1. INTRODUCTION 12
(a) Cezanne
(b) Monet
(c) Van Gogh
(d) Rembrandt
Figure 1.3.1: A sample work from each artist
fore culled from the Metropolitan Museum of Art’s Open Access to Scholarly Content
program [1].
1.3.3 Potential Problems
Drawing all images from the same source should control for any problems in image digiti-
zation, as one would assume all images from the same reputable source have the same scan-
ning perimeters. All images should contain the same faults, if there are faults. Nonetheless,
various conundrums regarding image digitization still occur.
At high resolutions, even dust or particulate matter can affect a scan, and a certain
amount of dithering or, alternately, color banding may cause inaccuracy in the image
representation. Though this would not impact and would actually likely aid image cate-
1. INTRODUCTION 13
gorization, it would make the categorization inauthentic, relying on lossy compression or
failed scanning methods rather than artistic style.
1.3.3.1 Scanning Artifacts
Small aspects of a scan or picture can impact painting analysis, especially at high resolu-
tions. This is especially prominent during edge detection.
(a) Hand from Rembrandt’s
Flora
(b) Canny Edge Detector
without blur
(c) Canny Edge Detector
with Guassian blur
Figure 1.3.2: Inaccurate edges are detected without blur. See lines in upper left of subfigure
(b).
To remove this effect, a strong Gaussian blur (standard deviation of 2) is applied to the
image before edge information is gathered. This removes artifacts, but may destroy some
less essential line information. As an added benefit, this removes issues with craquelure,
or naturally occuring cracks that appear in oil paint over time.
More information on the Canny edge detector can be found in Section 3.2.1.
1.3.3.2 Scanning Variation
A significant problem with digitized paintings are their variability. Changes in light, time
of day, and scanner or camera type all influence the appearance of the image.
It is difficult to account for this problem. In this case, it is assumed that pictures taken
from the same sources will have a limited amount of signal interference, and that this
interference will be similar across all images.
1. INTRODUCTION 14
(a)
(b)
(c)
(d)
(e)
Figure 1.3.3: Five distinct samples of Cezanne’s Mont Sainte-Victoire with Large Pine,
taken from Google Images.
(a) Hue Histogram (b) Saturation Histogram (c) Value Histogram
Figure 1.3.4: The variety between all five images is easily visible in the color histograms.
1.4 A Brief Overview
The target goal of this project is to successfully classify paintings by artist. There are
two necessary components of this task that appear in virtually all research of it: feature
collection and classification [2] [8] [9] [12].
1.4.1 Feature Sets
Other approaches into painting classification will consider different information about each
painting. Since the premise of this paper is to compare different types of texture analysis
(as a surrogate for brushstroke detection), the other features collected were nominal, but
still enough for substantially accurate classification to take place. Color information, edge
information, and two distinct forms of texture information were gathered. The resulting
information was condensed into a 128-feature vector which was then used for classification.
A sample data entry can be found in the appendix.
1. INTRODUCTION 15
1.4.2 Classification
The problem of classification means assigning data the correct one of a set of category
labels, utilizing a set of training examples that are already correctly assigned a label.
Various types of classification algorithms and data structures have been proposed. Some
research papers in image analysis make it their goal to discover which classification algo-
rithm succeeds best for the given data [2].
Since the aim of the paper is to compare methods of texture analysis, only one classifi-
cation algorithm need be used. Random forests were used, for reasons discussed in section
4.1.
2
Previous Work
Painting analysis is a relative novel field, even if it built off of the much older and theoretical
fields of texture analysis, image analysis, and classification. The first literature, focusing
mostly on digital restoration, began to appear sporadically in the late nineties [13]. Real
attempts at accurate classification didn’t see publication until the 2000s. This is certainly
not because the technologyisn’t available (although classification problems on such a large
scale are still seeing significant refinement). To speculate on the recent trend, there was
not yet significant economic pressure or means for easy implementation. The presence of
computer science as a pursuit of humanities, too, was still lacking.
Reviewing the painting classification literature of the past 15 years gives insight into
some of the primary categorization and feature extraction methods, as well as communi-
cating what is lacking or still unconsidered in the field.
2.1 Features Used
Much of the starting literature focuses on achieving classification that is as accurate as
possible. The theme generally seems to be to throw as many features as possible at a
2. PREVIOUS WORK 17
classifier, and hope it is resilient to any noise that may occur, or that the new information
in the data set will at least be distinct enough to compensate for it.
Color features are virtually always considered, and are thought of as the ’basic’ features
of painting analysis [2].
When accuracy is the primary motivation of the paper, a set of features make a con-
sistent reappearance, most of which do not relate intrinsically to the texture of the im-
age. These are SIFT, Color Histograms, Histogram of Gradients (HoG), and Saliency
Maps [12] [2]. There are other suggested features, including texture analysis methods. Ga-
bor filters are occasionally used in a non-texture classification mechanism called ’spatial
features’, and Fourier analysis was also promoted as a ’good feature’ [14].
In general, when desiring accuracy, more distinct features are better than fewer.
2.2 Categorization
In efforts to accurately categorize paintings, different categorization methods were used.
Researchers used the Naive Bayes Classifier, the SVM classifier, and random forests, and
routinely found the three perform increasingly better, respectively [2] [12]. The distinction
in performance was as drastic as almost 10%.
The categorization problem can vary across research as well. More often then artist
classification problems, researchers consider problems within a single artist’s catalogue, or
dating a wide variety of works across time. The work of Hedges created a ’clock’ based on
mark to date Renaissance copperplates, disregarding specific artist information in favor
of roughly estimating dates of any given plate based on other samples [6] [13]. This works
best given the assumption of stylistic similarity across artist. The research of Johnson and
Jafarpour investigated paintings of Van Gogh, again classifying for dates of creation, but
this time aiming for extreme accuracy, and assuming reasonable diversity within just one
artist’s catalogue [9] [8].
2. PREVIOUS WORK 18
2.3 Painting Analysis With Gabor Filters
The work of Johnson et al. is probably the most investigative study of texture analysis in
reference to paintings (or less formally, brushstroke analysis) that has been published thus
far [9] [8]. In some ways, their mission is outside the scope of this paper, as they examine
the artist Van Gogh specifically, and attempt to date paintings and identify forgeries. But
it is this tight focus that inspires the depth of their work into texture recognition, using
the fundamental thesis that the stroke of each artist is the most telling attribute of his
work. Most significantly, the ”Maastricht” group’s method of investigating brushstroke
focused on Gabor wavelets. Information on wavelets can be found in section 3.3.3.
The work of the Maastricht group establishes the premise of scale and direction impor-
tance. Notably, Johnson references the kernel bank as ”multi-scale oriented Gabor wavelet
filters.” The Maastricht group used six orientations at four scales.
The Maastricht group created a summary statistic referenced as ’energy,’ which exists
for each pixel. The energy value is quite simple the sum of squared value obtained after
convolving the real and imaginary part of the Gabor wavelet, collectively known as a
Gabor filter.
Energy proves to be a uniquely idiosyncratic classifier in spite of its simplicity, varying
highly from painting to painting, and unwaveringly high when given a forgery. The value
of the system is likely due to the large kernel bank they used.
The Maastricht group here proposes more information can be constructed from this
simple summary statistic. Formerly, energy was averaged across all partitions of a painting,
but if one constructs a multidimensional histogram of the energy for each partition, greater
accuracy is possible. Though promising, it is not a near perfect system; Johnson notes the
research both failed to identify two of six Van Gogh forgeries, and incorrectly identified
two real Van Goghs as forgeries.
3
Feature Extraction
A variety of features were collected to be used in classification. The nature and type of
each feature collection method is described here.
3.1 Color Spaces
As discussed in section 1.2.1, pixels have specific method of representation. Traditionally, if
an image is grayscale, each pixel is represented by a byte of value 0-255. In most paintings,
however, color is of essential interest, and images will not be represented as such unless
specifically converted.
When collecting color data, it is essential to consider color space and collection method.
3.1.1 RGB & HSV
There is a large variety of color spaces for an image to be represented in, each of which
influences methods of representation and color conversion. The most traditional represen-
tation of color space is the RGB (red-green-blue) color space.
Every color in RGB-space is represented by 3-tuple (for red, green, and blue, respec-
tively), with each integer value representing a byte (an integer between 0 and 255), as in
3. FEATURE EXTRACTION 20
grayscale representation, but instead representing the degree of their respective color in
that image. As an example, a point in RGB-space at (x,y) valued at (0, 0, 0) would be
absolute black. A point valued at (255, 0, 0) would be absolute red. A point valued at
(255, 255, 255) would be absolute white. Since each value in the tuple is of the same value,
all colors available can be accurately contained within a cube of each side of length 255.
(a) RGB Cube exterior
(b) 2D HSV wheel for hue and
saturation
A less common color space is HSV (hue-saturation-value). As in RGB-space, a point
in this color space is represented by a 3-tuple, and both color spaces can represent vir-
tually all the same colors. HSV-space is bounded by a cylinder, rather than a cube. The
different method of representation allows different types of image processing and different
information about the image data to be presented.
Hue is defined in polar coordinates, and is therefore presented as an integer between 0
and 360. Hue represents the pure color type of a pixel. A dark or light red pixel has an
equivalent hue to a vibrantly red pixel. This is particularly useful when considering images
affected by shadow or lighting.
Saturation is represented by an integer value from 1 to 100, and is associated with the
purity, or whiteness, of the color. Saturation is defined as the distance away from the
center, or the length of the vector whose angle is determined by the hue. At the furthest
3. FEATURE EXTRACTION 21
distance is the ’absolute’ color, a ’pure’ red, yellow, etc. At the center (no distance) is pure
white. This can be effectively seen in Figure 3.1.1b
Value is defined along the z-axis of the space. At the bottom is black, and at the top
is, once again, the ’pure’ color value. An HSV-space pixel with a saturation and value of
100 will be an absolute color. If the saturation is valued at 0 and the value remains 100,
the color will be absolute white. If value is 0, the color will be absolute black, regardless
of the saturation or hue.
This means that a proposed pixel value of, say, (0,0,0) and (180, 99, 0) are equivalently
black. To compensate for the fact that multiple inputs can map to the same color, a
simple change is made to the conversion process to convert the proposed saturation value
to chroma. Chroma is value-dependant, and its range of possible values decreases relative
to the value. The color space is now represented in a cone, which can fit inside of the
cylinder representing HSV-space. This method of representation was used in the wavelet
based research of Jafarpour et al [9].
While notable, chroma is not being used in this instance. HSV is sufficient, as it still
represents pixel values in Cartesian space, which is necessary for edge detection and image
processing, and provides a more intuitive and perceptual representation of color useful for
classification and understanding.
3.1.2 Conversion
The conversion from RGB-space to HSV-space is simple. Below is pseudocode that repre-
sents the method of transition from RGB-space to HSV-space.
method rgb2hsv(r, g, b)
//first calculations
ma = max(r, g, b)
mi = min(r, g, b)
c = ma - mi //c here can represent chroma
3. FEATURE EXTRACTION 22
//hue
if c == 0
h = undefined
else if ma == r
h = ( (g - b) / c ) % 6
else if ma == g
h = ( (b - r) / c) + 2
else if ma == b
h = ( (r - g) / c) + 4
hue = h * 60
//saturation
if ma == 0
sat = 0
else sat = c / ma
//value
val = ma
return (hue, sat, val)
3.1.3 Binning
Color, when available, usually serves an important role in image classification, and the
instance of painting classification is no different. Gathering color information can be a
complex task. The wide variety of color spaces is particularly enough to complicate the
issue. There is a wide variety of information traditionally used in the task, including
the ’percentage’ of dark colors (here represented in ’value’), the range of color ’peaks’,
and the ’skew’ of color, or deviation of the grey levels away from a standard Gaussian
distribution [7].
HSV-space is often the most effective color space for categorization, and with the image
having been converted, some sort of information about the image must now be gathered.
The most common means of doing so is called binning.
Binning is, in this context, the means of grouping data together into meaningful pre-
defined sets. It is a form of quantization. Binning is a common technique with myriad
3. FEATURE EXTRACTION 23
applications. They are used for hash tables, image resizing, and most research with large
data sets.
The types of bins in the case of HSV-space painting images is two-fold. For hue, values
are grouped in increments of 30, while saturation and value are grouped by increments
of 10. This yields 32 bins overall. The quantity of pixels belonging to each bin is then
normalized to one, giving the percentage likelihood of any one pixel belonging to that bin.
It is most like human-designated classification of color to group hue in some number
of groups n = 3 ∗ 2
x
where the size of each bin is 360/n. This is because of the natural
definition of hue. The entire color wheel, seen in Figure 3.1.1b, can be divided first into
3 bins, yielding the primary colors, and then 3 more, yielding secondary colors. 6 more
gives tertiary colors, 12 the quandary, and the process can continue until there is more
than one bin for each possible hue (when x = 7), after which continued binning would be
functionally useless.
Dividing into over 360 bins risks capturing for lighting variation and scanning artifacts
once more. The high dimensionality of the data would also risk confusing a classifier. 12
bins is picked as a happy medium, capturing color information while not including too
much information.
For saturation and value, 10 bins are chosen as an accompaniment to hue, being the
nearest whole to the number of hue bins that divides evenly into 100, the range of both
types of pixel color information. Were hue bin values to scale up or down, value and
saturation should accordingly.
Color can act as a strong classifier. Though most of the artists seem to follow the same
rough trend (which is intriguing in and of itself), significant enough distinctions between
artists become clear when their color choices are quantified in bins.
3. FEATURE EXTRACTION 24
Figure 3.1.2: Average color graphs for each artist normalized to 512x512 patch
3.2 Edge Detection
In addition to color, edges often prove to be a very strong basic indicator of the artist’s
hand [12] [9]. Like color, there are both a variety of means for detection and a variety of
types of information that can be garnered from edges. Edge detection, in this case, is not
detection for stroke, but rather for figure and division of space.
There are a variety of well-established and relatively simple methods for edge detection,
such as the Difference of Gaussians (DoG), the Laplacian of Gaussian (LoG), and the
Sobel filter, each of which depend, at least in part, on the act of convolution.
Extensive research has been performed on the value and significance of edge detectors
relative to one another [11] [10]. Though no choice could be reasonably deemed a failure,
3. FEATURE EXTRACTION 25
certain edge detectors are preferred. The edge detection algorithm used in this case is the
Canny edge detector. It was chosen for several reasons. Firstly, it routinely outperforms its
simpler and previous named counterparts, primarily DoG and LoG. Secondly, it provides
edge parameters as a binary matrix, providing clarity and strict definition of the edge.
Most importantly, its performance has a heavy degree of malleability. Various components,
including a Gaussian blur and hysteresis thresholding, are changeable to given parameters,
so experimentation for optimal performance is preferred. As seen in Figure 1.3.2, this
adaptability can be extremely beneficial.
3.2.1 The Canny Edge Detector
Firstly, a Gaussian blur is usually convolved about the image to remove noise. In this case,
the Gaussian blur was selected to be uncommonly strong, with a standard deviation of 2,
for reasons already discussed.
Let g equal an approximation of this blur, as used by the Canny filter. Let f equal the
a grayscale version of image in question.
g =
.035 .038 .040 .038 .035
.038 .042 .045 .042 .038
.040 .044 .047 .044 .040
.038 .042 .045 .042 .038
.035 .038 .040 .038 .035
(3.2.1)
f ∗ g = f
0
(3.2.2)
After this Gaussian blur is convolved with the image, the edge detector needs to identify
potential edge magnitudes and and directions. This is done with an edge detection operator,
traditionally with two Sobel filters, one for the x and y directions.
G
x
=
−1 0 1
−2 0 2
−1 0 2
∗ f G
y
=
1 2 1
0 0 0
−1 −2 −1
∗ f (3.2.3)
3. FEATURE EXTRACTION 26
Figure 3.2.1: Visual representation of a Guassian blur
Where G is the gradient strength, and θ is the edge direction.
G =
q
G
x
2
+ G
y
2
(3.2.4)
θ = arctan2(G
y
, G
x
) (3.2.5)
Theta is rounded off to the nearest multiple of 45, as edge direction can only be diagonal,
horizontal, or vertical.
The Sobel filter now yields the appearance of edges, but they are weighted rather than
binary. The definitive edge is not yet determined.
To accomplish this the process of edge thinning occurs. This uses theta to account for
any potential edge pixel’s two directional neighbours. If the point has a greater magnitude
(G), than it is considered a potential edge.
Lastly, there is the process of hysteresis thresholding. Whether or not a line is part of
an edge is in this case a neighbor-dependant problem. Simply put, a potential edge pixel
is more likely to be an edge if it is near other accompanying potential edge pixels. The
necessary magnitude of these potential edge neighbors is given by a previously determined
set of thresholds, high and low. If the potential edge pixel is above the high threshold, it
3. FEATURE EXTRACTION 27
is definitively an edge. If in between these the high and low parameters, and next to an
edge pixel, it is an edge. If below the low parameter, this pixel is not an edge.
(a) The Sobel filter
(b) The Canny edge detector
This is considerable in regards to painting, where edge detection can pick up changes in
stroke, lighting, and color changes in equal measure. If the threshold is set too low, even
with a strong Gaussian blur arbitrary edges will be picked up. If the distinction between
high and low thresholds is too large, lines will split off, accounting for parts of brushstroke
and accidental shifts in light. In this case, the low threshold is set to 15% of the maximum
intensity in the image. The high threshold is set to 20%.
After hysteresis thresholding, the image is now a binary matrix, indicating the edges of
the image relative to the blur and hysteresis threshold values given.
3.2.2 Line Features
After edge detection has been performed over the image, information on the edges still
needs to be gathered. Two primary statistics were used: edge length and edge count.
Edges were found by iterating across the image. On finding an edge point, the algorithm
would create an array representing the edge, add this pixel to the array, and perform this
operation again on any surrounding edge points. This means edge length is defined not by
the literal length of the edge, but rather the number of pixels that make up its construction.
Edge count is the number of edges found in a single image.
3. FEATURE EXTRACTION 28
The edge gathering mechanism is very similar to the problem of connected component
labelling. The image can be interpreted as a graph, where each ’True’ labeled pixel in
the edge detected image represents a vertex, and an edge exists between any of the eight
adjoining pixels. The labelling method used here is a simple single-pass algorithm.
Figure 3.2.3: Edge count and edge length for each artist
The high degree of variance in certain instances is generally unexplained, beyond that
of natural variation within an artist’s catalogue. Outliers as large as edge lengths over 75
and edge counts over 700 appear for specific paintings.
While these outliers may prove troublesome for classification, they tell us something
interesting about the image to which they belong, and the artist in general. A painting
like The Parc Monceau by Monet has the most edges per patch of any painting of all four
artists. For the extent to which edge count might stand in for complexity or information
density, this statistic might suggest The Parc Monceau is the most complex of Monet’s
entire catalogue.
3.3 Texture
Edge information may feel influence from stroke and texture, but it does not account
for either. For one, edge information does not account for direction. For another, edge
3. FEATURE EXTRACTION 29
Figure 3.2.4: This patch from The Parc Monceau has over 1000 edges. It might be con-
sidered the most complex patch from Monet’s work.
information does not account for types of transition, merely the fact that it occurs. For
instance, a black and white image would read the same edge information even if color
inverted, while the texture would be wildly different.
It is difficult to define texture, despite its ubiquity in visual experience. The concept of
texture is that, even with a stochastic process applied to it (e.g. noise, variation, shading)
there is an underlying deep structure and pattern to a material surface which aids in its
recognition.
3.3.1 Texture and Brushstroke
It is a fundamental assumption of this project that artists have an idiosyncratic texture
to their work. This texture is manifested not in the color, but in the brushwork of an
artist. This proposition has been repeatedly confirmed, as attempts to classify artists by
brushstroke have proven relatively successful, even allowing artworks within an individual
artist’s catalogue to be dated, and for potential forgery detection to take place [8].
3. FEATURE EXTRACTION 30
However, brushstroke is not precisely texture in painting, but rather an essential aspect
of it. To consider texture a more representative measure of brushstroke, factors like sizing
and lighting must be accounted for.
Even texture itself can only be purported as measured by various techniques. In re-
ality, the relationship any proposed computational measurement has to a more human
abstraction is never quite set in stone. It is only through experimentation that one can
really access the effectiveness of a texture measurement in actually representing texture.
R.M. Haralick makes note of this in the last appendix of his well-known texture-analysis
method, discussed below [5].
3.3.2 Haralick Features
Haralick features are a rather well known form of texture analysis, originally designed for
distinguishing bird’s-eye view images of crops and land. Their use in painting is fairly
limited, likely because of the remoteness of their original application from painting, but
not unheard of [12]. As a method of general texture analysis, they are often very successful,
but their capacity for a task as specific as painting is not well-known.
3.3.2.1 The Co-Occurrence Matrix
Haralick features are just summary statistics for a basic underlying data structure: the
co-occurrence matrix. It serves to measure the probability that any given pixel gray level
will appear adjacent to any other pixel gray level. The co-occurrence matrix is a square
matrix of length N
g
, where N
g
is the number of gray levels in the image (Haralick features
and texture analysis in general do not traditionally operate over a colored image). In this
instance, N
g
= 255, the standard for gray-level images.
Haralick features require iterating over every pixel in the image. In the co-occurrence
matrix, every row represents the gray level of the pixel being examined. Every column is
the gray-level of one of four possible neighboring pixels. In fact, Haralick features are built
3. FEATURE EXTRACTION 31
for four different co-occurrence matrices, one for each type of neighboring pixel: one each
θ at 0
o
, 45
o
, 90
o
, and 135
o
. This θ for neighboring pixels is vaguely similar to that used
for edge thinning in Canny edge detection, see section 3.2.1.
Figure 3.3.1: Potential pixel comparisons for a co-occurrence matrix
Of the eight possible neighbors of a pixel, the other four or not considered, as after
iterating over all pixels in the matrix, they would mirror the first four, with x and y values
flipped. No relationships could be garnered from them that could not be garnered from
the other four. Even the distinct co-occurrence matrices used, Haralick notes, “are four
closely-related measures.”
The border case is, as with convolution, a problem. In this case, values are simply not
tabulated where there is no pixel-neighbor relationship. The sum value of all cells in the
co-occurrence matrix, then, is the image length times image height, minus the image height
and/or width, depending on the pixel relationship used.
As an example, consider convolved image g in Figure 1.2.2. When normalized to 5 gray
levels, the image has four easily viewable co-occurrence matrices.
While the co-occurrence matrix has a wide variety of applications, it most regarded for
its classifying capabilities, using the the 14 summary statistics Haralick makes note of in
his first appendix.
3. FEATURE EXTRACTION 32
(a) image g (b) g normalized to N
g
= 5
0 0 2 3 3
0 0 2 3 4
0 1 3 3 3
1 2 3 3 3
0 1 2 2 2
(c) numeric representation of g
2 2 2 0 0
0 0 2 1 0
0 0 2 3 0
0 0 0 5 1
0 0 0 0 0
(a) 0
o
1 1 2 1 0
0 1 0 1 0
0 0 1 2 0
0 0 2 3 1
0 0 0 0 0
(b) 45
o
3 2 0 0 0
1 0 1 0 0
0 1 1 1 0
0 0 3 5 1
0 0 0 1 0
(c) 90
o
2 0 0 0 0
0 1 0 0 0
2 1 0 0 0
0 1 4 4 0
0 0 0 1 0
(d) 135
o
Figure 3.3.3: co-occurrence matrices for each neighbor relationship in g where N
g
= 5
3.3.2.2 Summary Statistics
14 summary statistics are commonly gathered for each co-occurrence matrix. The features
are merely suggestions as to how to summarize a co-occurrence matrix, but they are now
used routinely, and the classifying power of each depends on the problem in question.
They are as follows:
p(i, j) is the location of an entry in the co-occurrence matrix in row i, column j
p
x
(i) is the probability of i in the x column
p
x+y
(k) is the probability of any value where i + j equals k
N
g
is the number of gray levels in the image
Angular Second Moment:
N−1
X
i=0
N−1
X
j=0
p
i,j
2
3. FEATURE EXTRACTION 33
Angular Second Moment increases as any given entry in the co-occurrence matrix does.
This means it is largest when the image is most uniform. It is theoretical similar to the
’energy’ summary statistic used by the Maastricht group for Gabor wavelets [9].
Contrast:
N
g
−1
X
n=0
n
2
N
g
X
i=1
N
g
X
j=1
p
i,j
, |i − j|
Contrast measures the degree of distinction between neighboring pixels. Pixels that
move from pure black to pure white very quickly are prone to have higher values in this
feature.
Correlation:
P
N−1
i=0
P
N−1
j=0
(ij)P
i,j
− µ
x
µ
y
σ
x
σ
y
where µ
x
, µ
y
, σ
x
, and σ
y
are the means and standard deviations of p
x
and p
y
Correlation shows the linear dependency of a gray level. If certain gray levels appear
only when routinely next to other gray levels, correlation will be high.
Sum of Squares- Variance:
N−1
X
i=0
N−1
X
j=0
(i − µ)
2
p
i,j
Variance measures the dispersion of values across the image. For example, a black and
white image will have a relatively low variance (assuming N
g
is 255), because there are
few to no occurrences of other values.
Inverse Difference Moment:
N−1
X
i=0
N−1
X
j=0
1
1 + (i − j)
2
p
i,j
Inverse Different Moment is a measure of homogeneity. If the co-occurrence matrix is has
probabilities close to the diagonal, it will be high. Pixels must occur near pixels of the
same value.
3. FEATURE EXTRACTION 34
Sum Average:
2N
g
X
i=2
ip
x+y
(i)
where x and y are the coordinates of an entry in the occurrence matrix and p
x+y
(i) is
the probability co-occurrence matrix coordinates sum to x + y.
In general, ’Sum’ and ’Difference’ characteristics (Sum Entropy, Difference Variance,
etc.) measure mentioned characteristics across gray levels, that to say rows and columns
of the co-occurrence matrix, rather than in regards to specific pixel adjacencies. This gives
these statistics a greater generalizing power, and they may serve better as a summary
statistic in co-occurrence matrices with high N
g
levels.
Sum Variance:
2N
g
X
i=2
(i − f
6
)
2
p
x+y
(i)
N.B. In Haralick’s original paper, variance uses the eighth feature rather than the sixth.
This is assuredly a mistake, and has been corrected here.
Sum Entropy:
−
2N
g
X
i=2
p
x+y
(i)log
p
x+y
(i)
= f
s
Entropy is difficult to define, but it effectively measures the information density of an
image. It is similar to variance, but distinct. To reuse the black and white example, if an
image is binary white noise, the entropy will be high, because although not all values are
being used, values are distributed in a complex way.
Entropy:
−
N
g
−1
X
i=0
N−1
X
j=0
p
i,j
log
p
i,j
Difference Variance:
N
g
−1
X
i=0
i
2
p
x−y
(i)
Difference Entropy:
−
N
g
−1
X
i=0
p
x−y
(i)log
p
x−y
(i)
3. FEATURE EXTRACTION 35
Measure of Correlation 1:
HXY − HXY 1
max(HX, HY )
H here represents entropy, so HXY is literally the above entropy feature, HX and HX
the entropy of p
x
and p
y
, respectively, and HXY 1 = −
P
N
g
−1
i=0
P
N−1
j=0
p
i,j
log
p
x
(i)p
y
(j)
Measure of Correlation 2:
(1 − exp[−2(HXY 2 − HXY )])
1/2
where HXY 2 = −
P
N
g
−1
i=0
P
N−1
j=0
p
x
(i)p
y
(j)log
p
x
(i)p
y
(j)
The last characteristic, known as the Maximal Correlation Coefficient, depends
on drawing eigenvalues from the matrix, which is often computationally inefficient to
compute. It has been left out for this reason.
Accuracy rates in classification for all Haralick features considered collectively can be
found in table 4.3.1.
3.3.3 Gabor Filters
Gabor filters are the second method of texture analysis to be considered. They operate
via the process of convolution, as discussed the section 1.2.2. Gabor filters are particularly
useful for texture analysis because of the method of kernel generation, and the use of
multiple kernels.
3.3.3.1 The Gabor Wavelet
A wavelet is a signal that has a defined beginning and ending of zero. A sine wave, for
example, is not a wavelet, but a partition of a sine wave where the signal both begins and
ends at zero (for instance, [0,π]) is.
As discussed in section 1.2.1, a wavelet must be discrete in the instance of computational
representation. In this regard, a wavelet can be represented as an array of dimension n. A
3. FEATURE EXTRACTION 36
Gabor wavelet is simply a given signal multiplied by a Gaussian window, which is a given
range over any normal distribution.
f(x) = e
−(x−x
0
)
2
/a
2
e
−ik
0
(x−x
0
)
(3.3.1)
Formula for a Gabor wavelet
(a) sine wave (b) Gaussian window (c) Gabor wavelet
Figure 3.3.4: Visualization of a Gabor wavelet and its component parts
Gabor filters are two-dimensional kernels, which are seperable into two of these one-
dimensional Gabor wavelets. This underlying theory is key in generating a kernel for the
Gabor filter, but Gabor filters can be more practically thought of as edge detectors which
specifically react to edges of their given orientation and frequency.
3.3.4 Kernel Composition
The two-dimensional Gabor kernel is modeled by a theta, a frequency, and a sigma for the
x and y directions. Varying each changes the kernel type drastically. Each Gabor kernel is
not unlike a brushstroke, having direction and size.
Theta will vary the kernel orientation. Frequency controls for how often the signal
occurs. A high frequency yields a signal being repeated several times in a single kernel.
Sigma is the standard deviation of the sigma. A high sigma will yield a large Gabor kernel.
3.3.4.1 Kernel Bank
A key aspect of Gabor filters is that, commonly, more than one are used. A series of Gabor
kernels are assembled in what is collectively referred to as the kernel bank.
3. FEATURE EXTRACTION 37
Figure 3.3.5: A simple Gabor kernel, where θ = 0, σ = 1, and frequency is 3
The reasoning behind this is that the various qualities of a Gabor kernel react with an
image in different ways. A single kernel may hardly be descriptive of an entire image.
Figures 3.3.6 and 3.3.7 demonstrate Gabor filters of different orientation operating over
a patch taken from Van Gogh’s Cypresses. The patch effectively demonstrates the wide
variety of strokes that can be found in one painting, and the inability of any one Gabor
filter to adequately summarize any part of a painting.
The number of Gabor kernels necessary to reasonably define an image is never precisely
clear. The kernel bank containing the kernels used in this paper contains sixteen kernels,
with thetas varying in four directions, and two variable frequencies and sigmas. The kernel
bank is illustrated in figure 3.3.8.
3.3.4.2 Summary Statistics
As with co-occurence matrices, the image generated by Gabor filters cannot be used for
classification in and of themselves. Luckily, the summary statistics for an image filtered
by a Gabor kernel are much simpler. While a variety of valuable statistics can be taken
over the image, it is usually effective enough just to consider the mean and variance of
the values in the given image. Notably, these statistics are gathered over the image as
filtered by each of the sixteen kernels, for thirty-two features overall (as compared to the
52 features given by Haralick).
3. FEATURE EXTRACTION 38
(a) Original image (b) Combined θ
Figure 3.3.6: Original and edge detected image
(a) θ = 0
0
(b) θ = 45
0
(c) θ = 90
0
(d) θ = 135
0
Figure 3.3.7: Gabor filters operating over four common orientations
3. FEATURE EXTRACTION 39
Figure 3.3.8: Gabor filter kernel bank
4
Classification
After the feature set has been gathered, each feature is represented as a series of numeric
inputs. This means each color bin, Haralick or Gabor summary statistic, and piece of edge
information is considered separately in the classification process.
(a) Sample from Cezanne’s The Artist’s Uncle
[ 41086 193006 7723 2050 2431 2351 533 307 185 55 95 178 ]
(b) Array of binned hue values from sample
41086 193006 7723 2050 2431 2351 533 307 185 55 95 178
Red Ora. Y el. Char. Green Spr. Cyan Azu. Blue V io. Mag. Rose
(c) In classification, each value is considered individually with the attached label
Figure 4.0.1: Example of individual features for classification
4. CLASSIFICATION 41
The actual implementation of random forests is relatively simple, but the theoretical
underpinnings are not.
4.1 Random Forests
Random forests are remarkably resilient and successful in classification or regression anal-
ysis. They operate by generating a series of decision trees, and the decision trees act
collectively to pick a likely candidate class for the feature vector.
4.1.1 Decision Tree
The decision tree is the fundamental component of a random forest. Decisions about the
data are made at each edge, and each leaf has a label associated with it that concludes to
classification.
It should be known that decision trees can also generate numeric outcome rather than
enumerative. This is known as a regression tree. However, grouping paintings by artist
depends on class specification. This is called a classification tree.
4.1.2 Bootstrapping
Bootstrapping is a relatively simple but pivotal process by which random forests select a
sampling of the data to use in constructing a given decision tree within that forest.
Effectively, bootstrapping is sampling with replacement. From data set L containing N
samples in the form of {(x
n
, y
n
), n = 1...N}, where x and y are feature vectors and class
labels, respectively, draw L
(B)
samples. L
(B)
is sampled uniformly and with replacement.
This model can help repeatedly identify strong classifier variables from x, and can help
strongly improve unstable classifiers, like when the number of variables in x is greater
than N, which occurs often for painting analysis where painters have minimal or dubiously
authentic output. Generally, it helps to reduce variance and prevent overfitting in the data
as well.
4. CLASSIFICATION 42
Figure 4.1.1: Sample Decision Tree
Accurate measures of desirable size for L
(B)
and number of samples to draw can be
obtained experimentally [3]. Traditionally, L
(B)
is most dependant on the size of the data
set and the number of decision trees generated for the forest. Decision trees in a random
forest will not share the same L
(B)
, though both values will often be close.
4.1.3 Arboreal Voting
Each decision tree ’votes’ for its outcome on the given input x
n
, y
n
. The most voted
outcome is that selected by the random forest.
In the event decision trees voted on a numeric output, a simple averaging would occur.
It is not necessary to consider this case in artist classification.
4. CLASSIFICATION 43
4.2 A Collection Schema
In addition to the feature collection set, there are a variety of methods for collecting
these features. Different methods measure for the same qualities is distinct ways, yielding
different results. Since the classifier acts on these results, classification strength can vary
dramatically, although each schema is expected to perform with reasonable success . Three
methods are here considered: a generic model, where features are gathered across an entire
painting, a feature-dense model, where features are calculated across four parts of the
image and concatenated into a significantly larger feature vector, and a feature-specific
model, where features are calculated for small subsets of a given image, and then averaged
together in the final feature vector. 200 random forests were designed to fit the data, each
considering all available features at any given step in the decision tree creation. Their
collective performance is considered. Cross-validation was done to each to access accuracy
of categorization, using 5 folds.
4.2.1 Generic Model (The Entire Painting)
For the generic model, all features were found over an entire painting. The implication
of this is pretty clear. While color values should remain relatively constant (albeit scaled
up to a full painting) relative to the feature-specific model, edge lengths will be larger
and edge counts smaller. The impact of texture features will be seen. In the four-way
classification, the random forest routinely performs with 70% accuracy. Performance in all
two-way problems can be found on Figure 4.2.1 on page 46.
When moving onto the two-class problem, the sample size may get small enough that
overfitting becomes a serious issue, especially when there is a clear indicator variable or
variables, as in most of the Rembrandt-based classification. This consideration remains
across models.
4. CLASSIFICATION 44
4.2.2 Feature-Dense Model (Quadrants)
In the feature-dense model, every painting was divided into four equivalent parts. This
means that partitions analyzed may be of a different size across paintings. All color values
are normalized, but there is no clear way to account for how the texture features may
differ in classifying ability because of this, or if they will differ at all. It is proposed that
feature density may compensate for this, if there is enough correspondence between the
added features.
The feature-dense model uses a 472-feature vector, four times larger than the 118-feature
the other two models use.
The feature-dense model performs better, averaging 73% accuracy. The in-depth Figure
4.2.2 can be found on page 46.
4.2.3 Feature-Specific Model (Patches)
The feature-specific model deconstructs every painting into a small number of 512x512
patches and extracts features; features are later averaged together over all partitions of the
image. The resulting feature vector is of the same size of the generic model, but represents
an ’average’ 512 x 512 pixel block of the picture. Images are usually high-resolution enough
to offer anywhere from 25 to 35 blocks.
This form of feature collection is a much simplified version of that proposed by the Penn
State Group [9]. The premise is that at lower resolution pieces of an image allow for more
accurate measure of dissimilarity, improving the capacities of texture analysis and any
distance based measure. Color values are unaffected, and edge values should be impacted
in a roughly consistent way across all paintings, as certain edges once read as continuous
will be cut off by the cropped 512 x 512 patch.
4. CLASSIFICATION 45
The feature-specific model performs best in the four-way problem, and is the model
used, when not otherwise indicated, for other classification statistics in this paper. Its
general performance can be found on Figure 4.2.3 on page 46.
The feature-specific model notably performs worse in certain classifications, but provides
a more definitive overall model, performing well in all circumstances, while being less likely
to overfit to the given data.
4.3 Feature Comparison
Having tested various classification types, it is of utility to see more information on specific
classifiers. Namely, the value of each specific classifier should be clarified to ensure none
provide a useless signal or act as noise over the data set. It should also be considered which
specific features of classifying groups are most important.
4.3.1 Individual Features As Classifiers
It is important that as many features as possible help in classification, with the exception
of texture analysis, where it is anticipated both feature account for the same phenomenon,
with one eclipsing the other in terms of useful information.
It is necessary that individual features act in and of themselves as a better than random
classifier (about 25% in the 4-way problem), otherwise they are likely only adding noise
to the data set. Figure 4.3.1 demonstrates the classification prowess of each data category
in isolation (along the diagonal), and in union with any of the other data categories.
Much is confirmed from the data. All forms of feature collection prove themselves to
be better-than-random classifiers. As expected, one method of texture analysis is largely
eclipsed by the other. Gabor filters proves to be a worse indicator than Haralick features,
while not capturing for anything new when the features are combined. Surprisingly, sat-
4. CLASSIFICATION 46
Class Problem Accuracy Std. Dev.
4-way 70% 10%
Cezanne-Monet 73% 10%
Cezanne-Rembrandt 94% 4%
Cezanne-Van Gogh 78% 10%
Monet-Rembrandt 97% 4%
Monet-Van Gogh 55% 17%
Rembrandt-Van Gogh 100% 00%
Figure 4.2.1: Generic Model
Class Problem Accuracy Std. Dev.
4-way 74% 4%
Cezanne-Monet 78% 10%
Cezanne-Rembrandt 100% 0%
Cezanne-Van Gogh 82% 7%
Monet-Rembrandt 93% 10%
Monet-Van Gogh 63% 11%
Rembrandt-Van Gogh 100% 00%
Figure 4.2.2: Feature-Dense Model
Class Problem Accuracy Std. Dev.
4-way 79% 7%
Cezanne-Monet 72% 9%
Cezanne-Rembrandt 94% 7%
Cezanne-Van Gogh 89% 11%
Monet-Rembrandt 99% 2%
Monet-Van Gogh 78% 13%
Rembrandt-Van Gogh 100% 00%
Figure 4.2.3: Feature-Specific Model
4. CLASSIFICATION 47
4-Way Hue Sat. Value E. Count E. Length Haralick Gabor
Hue 46% - - - - - -
Sat. 43% 34% - - - - -
Value 64% 61% 57% - - - -
E. Count 57% 49% 58% 52% - - -
E. Length 57% 49% 68% 63% 41% - -
Haralick 65% 72% 65% 64% 78% 66% -
Gabor 63% 63% 60% 60% 75% 65% 58%
Figure 4.3.1: Accuracy of all pairings of features used in classification
uration values are largely without use, and edge length and Haralick features capture a
large portion of classifying power.
The results imply saturation values and Gabor values to be noise, and unsurprisingly,
when removed classification increases to just over 80%. The significantly smaller 76-feature
vector in this instance will be used when measuring feature importance.
4.3.2 Feature Importance
Random forests are also useful because they can give you measures of feature importance.
Feature importance can be measured in several ways. After a forest is fit to the data, all
samples in the training set are designated a value for out-of-bag error, or the likelihood
that they will be incorrectly classified by a tree in the forest that did not consider this
sample when generating.
For any given feature, the out-of-bag error is again measured with the variable in ques-
tion ”noised up,” or given artificially increased importance in the decision trees of the
random forest [4]. The difference between these two out-of-bag differences is the impor-
tance of the variable in question (with all importances being normalized). It is referred to
as ”permutation importance.”
4. CLASSIFICATION 48
A more common and related measure of feature importance is simply the raw impor-
tance, or the expected fraction of the sample any feature contributes to across all decision
trees. This is the importance estimate used here.
Figure 4.3.2: Graph of all 76 features’ importance measurements for one random forest
The running line represents the average value of all features. Along the x-axis, ranges
0-11, 12-21 represent hue and value bins, as explained in section 3.1.3. Values 22 and 23
represent edge count and length. All the following values represent Haralick features.
Feature importances become more clear if we graph and label the top ten features in
the importance array.
Figure 4.3.3: Features with the highest importance measurement
Edge length is the dominant important variable. Even though in 4.3.1 it serves as one
of the worst individual classifiers, it contains the most unique information.
4. CLASSIFICATION 49
Two of Haralick’s features specifically routinely serve as excellent classifiers as well,
across all four co-occurrence matrices that are constructed. These are Sum Entropy and
the first Measure of Correlation, respectively.
4.3.3 The Strong Classifiers
Considering only these particularly salient classifying variables allows an interesting study
to take place, with easy visualization that couldn’t be obtained from the normal feature
set, given its high dimensionality.
As suggested by figures 3.2.3 and 4.3.1, edge length is, of its own accord, a relatively poor
classifier. But when visualized with either of the two well-classifying Haralick features, the
value it offers becomes much more clear.
Figure 4.3.4: Measure of Correlation as a function of Edge Length
Edge length helps to clearly delineate the normally quite difficult Van Gogh-Monet
classification problem, while the information measure of correlation helps to distinguish
Cezanne. Rembrandt is, notably, spread across all the other data. The Rembrandt classi-
fication problem seems largely accounted for by Sum Entropy.
4. CLASSIFICATION 50
Figure 4.3.5: Sum Entropy as a function of Edge Length
While the information measure of correlation and sum entropy do well to delineate
Cezanne and Rembrandt, the Van Gogh-Monet problem becomes confused.
Figure 4.3.6: Sum Entropy as a function of Measure of Correlation
All three figures have the added benefit of visually explaining where confusions and
outliers in the data lie. Most artist groupings have at least one painting which, while
4. CLASSIFICATION 51
not necessarily being incorrectly classified, appear distinct from the other data of its set.
Discovering what these paintings are provides a painting from the artist’s catalogue which
is apparently distinct from the others. Bare in mind that these paintings are not distinct
in the more normal human registers, primarily that of color, but are rather distinct in the
texture and shape of the the figures in the image.
To find these images, the measures across all three graphs were normalized to one,
and the Euclidean distance between each painting and the mean value of all paintings in
that artist set were calculated. The painting with the largest distance is considered most
exceptional.
In all graphs 4.3.4, 4.3.5, and 4.3.6, there is a clear outlier in the Cezanne group. This
painting is Cezanne’s Madame Cezanne in a Red Dress.
Rembrandt also has a notable outlier in graphs 4.3.4 and 4.3.6, along the Measure of
Correlation statistic. This painting is Rembrandt’s Aristotle with a Bust of Homer.
Information on Monet is rather well dispersed, and thus difficult to classify. In graph
4.3.4, there is a suggestion of three mild outliers. The greatest among these is Camille
Monet on a Garden Bench.
Van Gogh is very well clustered across all graphs, suggesting a style both well-defined
and idiosyncratic. Nonetheless, the closest painting to an outlier in his data set is La
Berceuse.
Abnormal paintings could be determined for any of the characteristics used by the clas-
sifier, but since they have been determined given the three routinely strongest classifying
attribute, it is these paintings that are exceptional in regards to the most characteristic
measures of each artist.
4. CLASSIFICATION 52
(a) ...in a Red Dress
(b) Aristotle
(c) La Berceuse
(d) ...on a Garden Bench
Figure 4.3.7: Relatively abnormal paintings from each of the four artists
5
Conclusions
It is clear in both this experiment and other literature on the topic that significantly accu-
rate painting classification is possible. Access to large and relevant feature sets alongside
advanced classification algorithms are making the task progressively easier, and so re-
searchers continue to move steadily towards forgery detection and empirically determined
catalogue raisonn´es.
A difficulty in this task is that human performance can never reasonably be 100%
accurate. A success rate of above 80% is beyond expectations, and shows the value of even
basic feature collection, as well as texture analysis.
The task can also serve to empirically illuminate distinctions between artists, and within
an artist’s catalogue. Specific works can be distinguished for their abnormality, and suggest
a change in style or painting application.
5.1 Texture for Painting Classification
Texture is of clear value when considering a painting’s authorship. Research even begins
to suggest texture analysis to be even more essential to the question of authorship than
5. CONCLUSIONS 54
more readily apparent characteristics, like shape and color, as both Haralick features and
Gabor filters performed better in isolation than any other feature collected (cf. 4.3.1).
Haralick features prove themselves as better classifiers than Gabor filters in this specific
four way problem, but it is important to note potential reasons for this, especially after
Gabor filters have proven to perform quite well in other instances [8] [9].
The size and type of Gabor kernels found in the Gabor kernel bank is one clear justi-
fication for this. Larger and more varied kernels may yield more useful classifying data.
The summary statistics used may be another answer. As noted in section 2.3, the Maas-
tricht group found significant success with the ’energy’ statistic, but only in distinguishing
work with an artist’s catalogue, not between artists. Other summary statistics should be
considered as well.
Haralick features also raise the question of adaptability. While the two features of Mea-
sure of Correlation 1 and Sum Entropy serve well to classify the given four artists, does
this remain true for new works, and new artists? The nature of Haralick features suggests
they are adaptable to a wide variety of instances, but in higher and different class prob-
lems, they may show themselves to fail. Nonetheless, Haralick features should likely be
considered in basic classification problems before Gabor filters.
5.2 Future Work
Given that even human completion of the painting classification task will never be perfect,
there is always room for continued research in the field.
Forgery detection and genre classification has already been suggested and tackled, with
a degree of success. A particularly valuable insight would be in the form of optimization
of feature classification strength, and feature collection models. Section 4.2 suggests the
’patchwork’ approach is best for analysis, but at what scale do telling features emerge?
Would it be helpful, for example, to consider 128 x 128 pixel patches rather than the
5. CONCLUSIONS 55
given 512 x 512? In terms of feature collection, what, empirically, is the optimal sigma
for blurring during edge detection? What is the optimal size and variation to find in the
Gabor kernel bank?
For brushstroke analysis, it is certainly of most value to consider the highest reso-
lution images. But for qualities of color, edge, and a more general texture for broader
classification, it may be of more value to consider the responsiveness of lower resolution
representations of the image, or lower representation patches. The Laplacian or Gaussian
image pyramid is suggested, whereby each image is blurred with that pyramid’s respective
filter, before the image resolution is halved, until no information of value can reasonably
be obtained.
More than inventing new methods of classification, this research would tellingly explain
how to best collect feature information using known techniques.
6
Appendix
6.1 Data Format
Gathering features over high-resolution paintings is a time-consuming task. The process
itself can be hastened by parallelizing the job, but it is still a waste of time to retabulate
statistics for a small change or to create a graphic. For this reason, data was written to
a text file, which was then read in by a seperate program for graphing and classification
purposes.
Every comma(,) represents a new array, while every space represents a new value in the
array. The sequence of the data for each analyzed element was as such: For labelling, the
artist, the painting, and the partition of the painting (as determined by the directory the
painting file was located at) would begin the data. The numeric data would follow: hue
bins, saturation bins, value bins, edge information, an array each for the thirteen Haralick
features from each co-occurrence matrix, and an array each for each of the two summary
statistics from the sixteen Gabor filters.
In the instance of the feature dense (quadrant) model, the numeric data would appear
3 more times, each representing a different quadrant of the given picture.
6. APPENDIX 57
6.2 Data Sample
The following is a data sample from the feature specific (patches) model of classification,
as it was the most successful method. Also shown is the breakdown of the data: the specific
value, the significance of that data, and how it is labelled for feature importance graphing.
Feature importance labels are often not entirely self-descriptive for the sake of brevity, as
these labels were used to label the x-axis in Figure 4.3.3
Figure 6.2.1: Sample Image from Cezanne The Card Players
6. APPENDIX 58
Cezanne, TheCardPlayers, TheCardPlayers-5.jpg, 9965.0 15517.0 5521.0 14050.0
28877.0 51401.0 114389.0 8170.0 1256.0 220.0 107.0 527.0, 106365.0 71656.0 45412.0
17099.0 4884.0 3227.0 1270.0 87.0 0.0 0.0, 0.0 3161.0 10297.0 13784.0 16730.0
114909.0 85817.0 4709.0 593.0 0.0, 56, 67.3035714286, 0.00129129158517 43.7771422846
0.9726282171 799.676485157 0.253600529958 266.546857715 3154.92879834 7.31863387617
10.8121925641 0.000470838516473 3.66964213557 -0.296717583836 0.98837221376,
0.00105617486853 67.2912397942 0.957988562297 800.868090621 0.209530286534
266.501443769 3136.18112269 7.30549348478 11.0982683699 0.000384127938241
3.95594347081 -0.252149452314 0.979451134551, 0.00157654353999 30.503511022
0.980940589289 800.221777193 0.298030637423 266.542533066 3170.38359775
7.32899668582 10.5418480673 0.00057197799843 3.40851201006 -0.339831749943
0.993299440861, 0.00107190739164 58.4635162108 0.963499880732 800.867468145
0.213872411241 266.501427705 3145.00635637 7.30895674208 11.0420581836
0.000397026105889 3.88833877836 -0.261001015334 0.981656320455, 0.499142295394
0.0106388381711, 0.33670532125 0.00468260706386, 0.152590494966 0.00105987352289,
0.000502239456194 8.54221417217e-06, 0.49914672401 0.0106368002851, 0.339621190183
0.00470670196224, 0.152804272225 0.00104881742826, 8.08921440868e-05
5.8152160312e-06, 0.499142295394 0.0106320597617, 0.33670532125 0.00456344304993,
0.152590494966 0.00103242625921, 0.000502239456194 7.72652861089e-06, 0.49914672401
0.0106344078758, 0.339621190183 0.00467721292324, 0.152804272225 0.00103757783919,
8.08921440869e-05 3.91802350991e-06
Figure 6.2.2: Sample Image Data
6. APPENDIX 59
Artist: Cezanne
Painting: TheCardPlayers
Partition: TheCardPlayers-5
Hue:
9965 15517 5521 14050 28877 51401 114389 8170 1256 220 107 527
Red Ora. Y el. Char. Green Spr. Cyan Azu. Blue V io. M ag. Rose
The labels for feature importance are the same as the meanings above
Saturation:
106365 71656 45412 17099 4884 3227 1270 87 0 0
0 − 09 10 − 19 20 − 29 30 − 39 40 − 49 50 − 59 60 − 69 70 − 79 80 − 89 90 − 99
sat0 sat1 sat2 sat3 sat4 sat5 sat6 sat7 sat8 sat9
Value:
0 3161 10297 13784 16730 114909 85817 4709 593 0
0 − 09 10 − 19 20 − 29 30 − 39 40 − 49 50 − 59 60 − 69 70 − 79 80 − 89 90 − 99
val0 val1 val2 val3 val4 val5 val6 val7 val8 val9
Edge Count:
56
E. Count
Edge Length:
67.3035714286
E. Length
Haralick Features:
Co-Occurence Matrix 0 (Left-Diagonal):
0.00129129158517 43.7771422846 0.9726282171 799.676485157 0.253600529958
ASM Contrast Correlation V ariance IDM
har0 − 0 har0 − 1 har0 − 2 har0 − 3 har0 − 4
266.546857715 3154.92879834 7.31863387617 10.8121925641 0.000470838516473
Sum Average Sum V ariance Sum Entropy Entropy Difference V ariance
har0 − 5 har0 − 6 har0 − 7 har0 − 8 har0 − 9
3.66964213557 −0.296717583836 0.98837221376
Difference Entropy Measure of Correlation 1 Measure of Correlation 2
har0 − 10 har0 − 11 har0 − 12
Co-Occurence Matrix 1 (Left-Right):
0.00105617486853 67.2912397942 0.957988562297 800.868090621 0.209530286534
ASM Contrast Correlation V ariance IDM
har1 − 0 har1 − 1 har1 − 2 har1 − 3 har1 − 4
266.501443769 3136.18112269 7.30549348478 11.0982683699 0.000384127938241
Sum Average Sum V ariance Sum Entropy Entropy Difference V ariance
har1 − 5 har1 − 6 har1 − 7 har1 − 8 har1 − 9
3.95594347081 −0.252149452314 0.979451134551
Difference Entropy Measure of Correlation 1 Measure of Correlation 2
har1 − 10 har1 − 11 har1 − 12
6. APPENDIX 60
Co-Occurence Matrix 2 (Up-Down):
0.00157654353999 30.503511022 0.980940589289 800.221777193 0.298030637423
ASM Contrast Correlation V ariance IDM
har2 − 0 har2 − 1 har2 − 2 har2 − 3 har2 − 4
266.542533066 3170.38359775 7.32899668582 10.5418480673 0.00057197799843
Sum Average Sum V ariance Sum Entropy Entropy Difference V ariance
har2 − 5 har2 − 6 har2 − 7 har2 − 8 har2 − 9
3.40851201006 −0.339831749943 0.993299440861
Difference Entropy Measure of Correlation 1 Measure of Correlation 2
har2 − 10 har2 − 11 har2 − 12
Co-Occurence Matrix 3 (Right-Diagonal):
0.00107190739164 58.4635162108 0.963499880732 800.867468145 0.213872411241
ASM Contrast Correlation V ariance IDM
har3 − 0 har3 − 1 har3 − 2 har3 − 3 har3 − 4
266.501427705 3145.00635637 7.30895674208 11.0420581836 0.000397026105889
Sum Average Sum V ariance Sum Entropy Entropy Difference V ariance
har3 − 5 har3 − 6 har3 − 7 har3 − 8 har3 − 9
3.88833877836 −0.261001015334 0.981656320455
Difference Entropy Measure of Correlation 1 Measure of Correlation 2
har3 − 10 har3 − 11 har3 − 12
Gabor Kernel:
θ = 0, freq. = .05, σ = 1:
0.499142295394 0.0106388381711
Mean V ariance
gab0 − 0 gab0 − 1
θ = 0, freq. = .05, σ = 3:
0.33670532125 0.00468260706386
Mean V ariance
gab1 − 0 gab1 − 1
θ = 0, freq. = .03, σ = 1:
0.152590494966 0.00105987352289
Mean V ariance
gab2 − 0 gab2 − 1
θ = 0, freq. = .03, σ = 3:
0.000502239456194 8.54221417217e − 06
Mean V ariance
gab3 − 0 gab3 − 1
6. APPENDIX 61
θ = 45, freq. = .05, σ = 1:
0.49914672401 0.0106368002851
Mean V ariance
gab4 − 0 gab4 − 1
θ = 45, freq. = .05, σ = 3:
0.339621190183 0.00470670196224
Mean V ariance
gab5 − 0 gab5 − 1
θ = 45, freq. = .03, σ = 1:
0.152804272225 0.00104881742826
Mean V ariance
gab6 − 0 gab6 − 1
θ = 45, freq. = .03, σ = 3:
8.08921440868e − 05 5.8152160312e − 06
Mean V ariance
gab7 − 0 gab7 − 1
θ = 90, freq. = .05, σ = 1:
0.49914672401 0.0106368002851
Mean V ariance
gab8 − 0 gab8 − 1
θ = 90, freq. = .05, σ = 3:
0.33670532125 0.00456344304993
Mean V ariance
gab9 − 0 gab9 − 1
θ = 90, freq. = .03, σ = 1:
0.152590494966 0.00103242625921
Mean V ariance
gab10 − 0 gab10 − 1
θ = 90, freq. = .03, σ = 3:
0.000502239456194 7.72652861089e − 06
Mean V ariance
gab11 − 0 gab11 − 1
θ = 135, freq. = .05, σ = 1:
0.49914672401 0.0106368002851
Mean V ariance
gab12 − 0 gab12 − 1
θ = 135, freq. = .05, σ = 3:
0.339621190183 0.00467721292324
Mean V ariance
gab13 − 0 gab13 − 1
θ = 135, freq. = .03, σ = 1:
0.152804272225 0.00103757783919
Mean V ariance
gab14 − 0 gab14 − 1
θ = 135, freq. = .03, σ = 3:
8.08921440869e − 05 3.91802350991e − 06
Mean V ariance
gab15 − 0 gab15 − 1
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